Data update

Task/Aliquot-sequence-classifications/JavaScript/aliquot-sequence-classifications.js

@@ -0,0 +1,81 @@
+// See https://en.wikipedia.org/wiki/Divisor_function
+function divisorSum(n) {
+    let total = 1n;
+    let power = 2n;
+    // Deal with powers of 2 first
+    for (; n % 2n === 0n; power *= 2n, n /= 2n) {
+        total += power;
+    }
+    // Odd prime factors up to the square root
+    for (let p = 3n; p * p <= n; p += 2n) {
+        let sum = 1n;
+        for (power = p; n % p === 0n; power *= p, n /= p) {
+            sum += power;
+        }
+        total *= sum;
+    }
+    // If n > 1 then it's prime
+    if (n > 1n) {
+        total *= n + 1n;
+    }
+    return total;
+}
+
+// See https://en.wikipedia.org/wiki/Aliquot_sequence
+function classifyAliquotSequence(n) {
+    const limit = 16;
+    const terms = new Array(limit);
+    terms[0] = n;
+    let classification = "non-terminating";
+    let length = 1;
+
+    for (let i = 1; i < limit; ++i) {
+        ++length;
+        terms[i] = divisorSum(terms[i - 1]) - terms[i - 1];
+
+        if (terms[i] === n) {
+            classification =
+                (i === 1 ? "perfect" : (i === 2 ? "amicable" : "sociable"));
+            break;
+        }
+
+        let j = 1;
+        for (; j < i; ++j) {
+            if (terms[i] === terms[i - j]) {
+                break;
+            }
+        }
+
+        if (j < i) {
+            classification = (j === 1 ? "aspiring" : "cyclic");
+            break;
+        }
+
+        if (terms[i] === 0n) {
+            classification = "terminating";
+            break;
+        }
+    }
+
+    let output = `${n}: ${classification}, sequence: ${terms[0]}`;
+    for (let i = 1; i < length && terms[i] !== terms[i - 1]; ++i) {
+        output += ` ${terms[i]}`;
+    }
+    console.log(output);
+}
+
+function main() {
+    for (let i = 1n; i <= 10n; ++i) {
+        classifyAliquotSequence(i);
+    }
+
+    const specialNumbers = [11n, 12n, 28n, 496n, 220n, 1184n, 12496n, 1264460n, 790n, 909n, 562n, 1064n, 1488n];
+    for (const i of specialNumbers) {
+        classifyAliquotSequence(i);
+    }
+
+    classifyAliquotSequence(15355717786080n);
+    classifyAliquotSequence(153557177860800n);
+}
+
+main();